Quantum Search in a non-Markovian environment

Abstract

This thesis explores the effects and origins of a ‘noise with memory’ in the dynamics of an open quantum system. The system considered here is a multi-qubit register performing the Grover’s quantum search algorithm. We show that a Markovian-correlated noise can enhance the efficiency of the algorithm over a time-correlation-less noise. We also analytically find the set of necessary and sufficient conditions for the algorithm’s success probability to remain invariant with respect to the number of noisy sites in the register and point out that these conditions hold irrespective of the presence of time-correlations in the noise. We then investigate the origins of the type of noise considered. In this regard, a ‘collisional model’ is constructed that exactly reproduces the noisy evolution of the open system. Non-Markovianity in the system’s evolution is then assessed using two well-known measures and they are shown to be non-coincident. Our model is then slightly modified to accommodate an elementary thermal bath. We then show that increasing the bath’s temperature increases information drainage from the system.